Abstract
The process of focusing of an inhomogeneously polarized beam passed through a system consisting of a uniaxial crystal and a polarization filter is considered. It is shown that the action of this system is equivalent to the action of a phase transparency with a complex relief of the refractive index. In particular, if the angle between the axes of the quarter-wave plate and the polarizer is equal to 45°, this transparency has a helicoidal relief. Simultaneously, two singular beams with different curvatures of their wavefronts arise in the transparency. The action of the lens consists in formation of a combined singular beam having three focal waists. The boundary wave arising upon focusing is able not only to form a new spectrum of toroidal vortices, but also to straighten the focusing region, forming a fairly extended range with a weak divergence.
Similar content being viewed by others
References
M. S. Soskin and M. V. Vastnetsov, Prog. Opt. 42, 219 (2001).
L. Allen, M. J. Padjett, and M. Babiker, Prog. Opt. 34, 291 (1999).
A. V. Volyar, Ukr. J. Phys. Opt. 3 (2), 69 (2002).
M. Berry, J. Mod. Opt. 45, 1845 (1998).
T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman, London, 1978; Mir, Moscow, 1980).
A. V. Volyar and T. A. Fadeeva, Opt. Spektrosk. 94, 260 (2003) [Opt. Spectrosc. 94, 235 (2003)].
R. B. Vaganov and B. Z. Katsenelenbaum, Fundamentals of the Diffraction Theory (Nauka, Moscow, 1982).
D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972; Mir, Moscow, 1974).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions (Nauka, Moscow, 1983).
Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. A. Stegun (National Bureau of Standards, Washington, 1964; Nauka, Moscow, 1979).
M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, Oxford, 1969; Nauka, Moscow, 1970).
G. N. Watson, Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge Univ. Press, Cambridge, 1952; Inostrannaya Literatura, Moscow, 1949).
O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
I. Freund, M. S. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
O. Bryngdahl, J. Opt. Soc. Am. 63, 1098 (1973).
Author information
Authors and Affiliations
Additional information
Translated from Optika i Spektroskopiya, Vol. 96, No. 1, 2004, pp. 107–116.
Original Russian Text Copyright © 2004 by Volyar, Fadeeva.
Rights and permissions
About this article
Cite this article
Volyar, A.V., Fadeeva, T.A. Focusing of singular beams. Opt. Spectrosc. 96, 96–105 (2004). https://doi.org/10.1134/1.1643993
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/1.1643993